NOTE: On April 2, 2018 I updated this video with a new video that goes, step-by-step, through PCA and how it is performed. Check it out!
https://youtu.be/FgakZw6K1QQ
RNA-seq results often contain a PCA or MDS plot. This StatQuest explains how these graphs are generated, how to interpret them, and how to determine if the plot is informative or not. I've got example code (in R) for how to do PCA and extract the most important information from it on the StatQuest website: https://statquest.org/2015/08/13/pca-clearly-explained/
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Step by step detail with example of Principal Component Analysis PCA
Read in more details - https://www.udemy.com/principal-component-analysis-pca-and-factor-analysis/?couponCode=GP_TR_1
Also if you just want to understand it high level without mathematics, you can refer to this link https://www.youtube.com/watch?v=8BKFd9izEXM

Principal Component Analysis, is one of the most useful data analysis and machine learning methods out there. It can be used to identify patterns in highly complex datasets and it can tell you what variables in your data are the most important. Lastly, it can tell you how accurate your new understanding of the data actually is.
In this video, I go one step at a time through PCA, and the method used to solve it, Singular Value Decomposition. I take it nice and slowly so that the simplicity of the method is revealed and clearly explained.
There is a minor error at 1:47: Points 5 and 6 are not in the right location
If you are interested in doing PCA in R see: https://youtu.be/0Jp4gsfOLMs
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Provides steps for carrying out principal component analysis in r and use of principal components for developing a predictive model.
Link to code file: https://goo.gl/SfdXYz
Includes,
- Data partitioning
- Scatter Plot & Correlations
- Principal Component Analysis
- Orthogonality of PCs
- Bi-Plot interpretation
- Prediction with Principal Components
- Multinomial Logistic regression with First Two PCs
- Confusion Matrix & Misclassification Error - training & testing data
- Advantages and disadvantages
principal component analysis is an important statistical tool related to analyzing big data or working in data science field.
R is a free software environment for statistical computing and graphics, and is widely used by both academia and industry. R software works on both Windows and Mac-OS. It was ranked no. 1 in a KDnuggets poll on top languages for analytics, data mining, and data science. RStudio is a user friendly environment for R that has become popular.

#PrincipalComponentAnalysis | Learn more about our analytics programs: http://bit.ly/2EtxyQM
This tutorial helps you understand the basics of Principal Component Analysis and its applications in Data Analytics.
#DataMining #MachineLearning #DataAnalytics #PCS
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You asked for it, you got it! Now I walk you through how to do PCA in Python, step-by-step. It's not too bad, and I'll show you how to generate test data, do the analysis, draw fancy graphs and interpret the results. If you want to download the code, it's here:
https://statquest.org/2018/01/08/statquest-pca-in-python/
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Lecture Series on Neural Networks and Applications by Prof.S. Sengupta, Department of Electronics and Electrical Communication Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

This is part of an online course on covariance-based dimension-reduction and source-separation methods for multivariate data. The course is appropriate as an intermediate applied linear algebra course, or as a practical tutorial on multivariate neuroscience data analysis.
More info here: https://www.udemy.com/dimension-reduction-and-source-separation-in-neuroscience/?couponCode=DRSS-3D5

Watch [Part 6] of Machine Learning With Python Tutorial for Beginners: https://www.youtube.com/watch?v=9c38Ga9EAc4
Visit https://greatlearningforlife.com and watch 100s of hours of similar high quality FREE learning content on Machine Learning, AI, Data Science, Deep Learning and more.
In Part 5 you will continue learning about Unsupervised Learning and focus on a specific clustering technique called Principal Component Analysis or PCA. You will understand the technique in detail through a business example.
#MachineLearning #MachineLearningWithPython #PythonMachineLearning #Python #PrincipalComponentAnalysis
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Principal Component Analysis Tutorial | Python Machine Learning Tutorial Part 3
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Machine learning algorithm typically finds the pattern and relationships in data without human intervention but the data that the machine learning algorithm had to deal with are usually very high dimensional.
Welcome back to another session of Machine Learning Algorithms in Python tutorial powered by Acadgild. In the previous video, you have learned the linear regression. If you have missed the previous, please check the links as follows.
Simple Linear Regression - https://www.youtube.com/watch?v=iL_iWFSzjK8&t=7s
Implementing Linear Regression in Python - https://www.youtube.com/watch?v=M1mzE1IT-Is&t=225s
In this machine learning tutorial, you will be able to learn Principal Component Analysis in python. Principal Component Analysis is a data pre-processing technique that allows the data to be transformed from higher dimensional space to a lower dimensional space in such a way that information that is crucial to drawing conclusions about the data is not lost.
So, What Exactly is Principal Component Analysis (PCA)?
• Principal Component Analysis (PCA) is a dimensionally-reduction technique that is often used to transform a high-dimensional dataset into smaller-dimensional subspace
• PCA is mathematically defined as an orthogonal linear transformation that transforms the data to a new coordinate system such that the greatest variance by some projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on.
What are Principal Components?
• Directions in which the data has the most variance – directions in which the data is most spread out
• Mathematically, Eigenvectors of the symmetric covariance matrix of the original dataset
• Each Eigenvector has the corresponding Eigenvalue. The Eigenvalue is a scalar that explains how much variance there is in the corresponding Eigenvector direction.
Applications of Principal Component Analysis (PCA)
• Compression
• Visualization of high dimensional data
• Speeding up of machine learning algorithms
• Reducing noise from data
Using Principal Component Analysis (PCA) for Compression:
Once Eigenvectors are computed, compress the dataset by ordering k eigenvectors according to largest eigenvalues and compute Axk
Reconstruct from the compressed version. We can reconstruct the data back by using inverse transformation mathematically represented by Axk x k.T
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We've talked about the theory behind PCA in
https://youtu.be/FgakZw6K1QQ
Now we talk about how to do it in practice using R. If you want to copy and paste the code I use in this video, it's right here:
https://statquest.org/2017/11/27/statquest-pca-in-r-clearly-explained/
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Determining the efficiency of a number of variables in their ability to measure a single construct.
Link to Monte Carlo calculator: http://www.allenandunwin.com/spss4/further_resources.html Download the file titled MonteCarloPA.zip.

In this video, we look at how to run an exploratory factor analysis (principal components analysis) in SPSS (Part 1 of 6).
Youtube SPSS factor analysis
Principal Component Analysis
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Video Transcript: In this video we'll take a look at how to run a factor analysis or more specifically we'll be running a principal components analysis in SPSS. And as we begin here it's important to note, because it can get confusing in the field, that factor analysis is an umbrella term where the whole subject area is known as factor analysis but within that subject there's two types of main analyses that are run. The first type is called principal components analysis and that's what we'll be running in SPSS today. And the other type is known as common factor analysis and you'll see that come up sometimes. But in my experience principal components analysis is the most commonly used procedure and it's also the default procedure in SPSS. And if you look on the screen here you can see there's five variables: SWLS 1, 2 3, 4 and 5. And what these variables are they come from the items of the Satisfaction with Life Scale published by Diener et al. And what people do is they take these five items they respond to the five items where SLWS1 is "In most ways my life is close to my ideal;" and then we have "The conditions of my life are excellent;" "I am satisfied with my life;" "So far I've gotten the important things I want in life;" and then SWLS5 is "If I could live my life over I would change almost nothing." So what happens is the people respond to these five questions or items and for each question they have the following responses, which I've already input here into SPSS value labels: strongly disagree all the way through strongly agree, which gives us a 1 through 7 point scale for each question. So what we want to do here in our principal components analysis is we want to go ahead and analyze these five variables or items and see if we can reduce these five variables or items into one or a few components or factors which explain the relationship among the variables. So let's go ahead and start by running a correlation matrix and what we'll do is we're going to Analyze, Correlate, Bivariate, and then we'll move these five variables over. Go ahead and click OK and then here notice we get the correlation matrix of SWLS1 through SWLS5. So these are all the intercorrelations that we have here. And if we look at this off-diagonal where these ones here are the diagonal. And they're just a one because of variable is correlated with itself so that's always 1.0. And then the off-diagonal here represents the correlations of the items with one another. So for example this .531 here; notice it says in SPSS that the correlation is significant at the .01 level, two tailed. So this here is the correlation between SWLS2 and SLWS1. So all of these in this triangle here indicate the correlation between the different variables or items on the Satisfaction with Life Scale. And what we want to see here in factor analysis which we're about to run is that these variables are correlated with one another and at a minimum significantly so. Because what factor analysis or principal components analysis does is that it analyzes the correlations or relationships between our variables and basically we try to determine a smaller number of variables that can explain these correlations. So notice here we're starting with five variables, SWLS1 through five. Well hopefully in this analysis when we run our factor analysis we'll come out with one component that does a good job of explaining all these correlations here. And one of the key points of factor analysis is it's a data reduction technique. What that means is we enter a certain number of variables, like five in this example, or even 20 or 50 or what have you, and we hope to reduce those variables down to just a few; between one and let's say 5 or 6 is most of the solutions that I see. Now in this case since we have five variables we really want to reduce this down to 1 or 2 at most but 1 would be good in this case. So that's really a key point of factor analysis: we take a number of variables and we try to explain the correlations between those variables through a smaller number of factors or components and by doing that what we do is we get more parsimonious solution, a more succinct solution that explains these variables or relationships. And there's a lot of applications of factor analysis but one of the primary ones is when you're analyzing scales or items on a scale and you want to see how that scale turns out, so how many dimensions or factors doesn't it have to it.

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This is Matlab tutorial: principal component analysis . The main function in this tutorial is princomp. The code can be found in the tutorial section in http://www.eeprogrammer.com/. More engineering tutorial videos are available in eeprogrammer.com
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I perform a PCA on a set of six MSCI indices. First, I go download the data and import it into R with readxl. Then I look at the data and the returns with some very basic techniques like plotting the performance with ggplot and tidyquant. Later I perform a PCA and also apply a varimax transformation on the loadings (the eigenvectors). Lastly, I look at how an equal-weighted portfolio performed versus a portfolio with components selected based on the PCA/varimax results. It's not fully as desired but (we want higher Sharpe ratio of course), but interesting nevertheless.

Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables[clarification needed] into a set of values of linearly uncorrelated variables called principal components. If there are {\displaystyle n} n observations with {\displaystyle p} p variables, then the number of distinct principal components is {\displaystyle \min(n-1,p)} {\displaystyle \min(n-1,p)}. This transformation is defined in such a way that the first principal component has the largest possible variance (that is, accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it is orthogonal to the preceding components. The resulting vectors[clarification needed] are an uncorrelated orthogonal basis set. PCA is sensitive to the relative scaling of the original variables.
*********************************
To get certificate subscribe at: https://www.coursera.org/learn/pca-machine-learning/
============================
Topic Covered::
Mean values
Mean of a dataset
Variances and covariances
Variance of one-dimensional datasets
Variance of higher-dimensional datasets
Linear transformation of datasets
Effect on the mean
Effect on the (co)variance
Mean/covariance of a dataset + effect of a linear transformation
Dot product
Welcome to module 2
Dot product
Inner products
Inner product: definition
Inner product: length of vectors
Inner product: distances between vectors
Inner product: angles and orthogonality
Inner products and angles
Inner products of functions and random variables (optional)
Projections
LectureWelcome to module 3
LectureProjection onto 1D subspaces
Example: projection onto 1D subspaces
Projections onto higher-dimensional subspaces
Full derivation of the projection
Example: projection onto a 2D subspace
PCA derivation
Problem setting and PCA objective
Multivariate chain rule
Finding the coordinates of the projected data
Reformulation of the objective
Finding the basis vectors that span the principal subspace
PCA algorithm
Steps of PCA
PCA in high dimensions
Principal Components Analysis (PCA)
Other interpretations of PCA (optional)
********************************************************************
About this course: This course introduces the mathematical foundations to derive Principal Component Analysis (PCA),
a fundamental dimensionality reduction technique. We'll cover some basic statistics of data sets, such as mean values
and variances, we'll compute distances and angles between vectors using inner products and derive orthogonal
projections of data onto lower-dimensional subspaces. Using all these tools, we'll then derive PCA as a method
that minimizes the average squared reconstruction error between data points and their reconstruction.
At the end of this course, you'll be familiar with important mathematical concepts and you can implement PCA all by yourself.
If you’re struggling, you'll find a set of jupyter notebooks that will allow you to explore properties of the techniques and walk you
through what you need to do to get on track. If you are already an expert, this course may refresh some of your knowledge.
This examples and exercises require:
1. Some ability of abstract thinking 2. Good background in linear algebra
(e.g., matrix and vector algebra, linear independence, basis)
3. Basic background in multivariate calculus (e.g., partial derivatives, basic optimization)
4. Basic knowledge in python programming and numpy
Who is this class for: This is an intermediate level course.
It is probably good to brush up your linear algebra and python programming before you start this course.
******************************************************************
This course is created by Imperial College London
If you like this video and course explanation feel free to take the
complete course and get certificate from: https://www.coursera.org/specializations/mathematics-machine-learning
This video is provided here for research and educational purposes in the field of Mathematics. No copyright infringement intended. If you are content owner would like to remove this video from YouTube, Please contact me through email: [email protected]
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In this python for data science tutorial, you will learn about how to do principal component analysis (PCA) and Singular value decomposition (SVD) in python using seaborn, pandas, numpy and pylab. environment used is Jupyter notebook.
This is the 19th Video of Python for Data Science Course! In This series I will explain to you Python and Data Science all the time! It is a deep rooted fact, Python is the best programming language for data analysis because of its libraries for manipulating, storing, and gaining understanding from data. Watch this video to learn about the language that make Python the data science powerhouse. Jupyter Notebooks have become very popular in the last few years, and for good reason. They allow you to create and share documents that contain live code, equations, visualizations and markdown text. This can all be run from directly in the browser. It is an essential tool to learn if you are getting started in Data Science, but will also have tons of benefits outside of that field. Harvard Business Review named data scientist "the sexiest job of the 21st century." Python pandas is a commonly-used tool in the industry to easily and professionally clean, analyze, and visualize data of varying sizes and types. We'll learn how to use pandas, Scipy, Sci-kit learn and matplotlib tools to extract meaningful insights and recommendations from real-world datasets

Principal Component Analysis Tutorial Part 2 | Python Machine Learning Tutorial Part 4
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Hello and Welcome back to another session of Machine Learning Algorithms in Python tutorial powered by Acadgild. In the previous video, you have learned the Principal Component Analysis (PCA) and how it helps us. In this tutorial, you will learn, how principal component analysis can be used in 3 different applications and it can be implemented in python. If you have missed the previous video, please check the links as follows.
Principal Component Analysis Part 1 - https://www.youtube.com/watch?v=CeXxokx8izc
Check out the implementation of compression of data using principal component analysis
Kindly, go through the complete video and please like, share and subscribe the channel.
#PCA, #principalcomponentanalysis, #python, #datascience, #machinelearning
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It is easy to apply principal component analysis (PCA) in Excel with the help of PrimaXL, an add-in software.
In this episode, we discuss about visualization of high dimensional clusters.
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This video shows how to use PCA on a Stock/ETF Portfolio in Zoonova.com. It takes the Portfolio Correlation Matrix with a large set of variables as input and calculates PCA which reduces the dataset down to Principal Components, Eigenvectors and Eigenvalues.